Manawatu would build up a points leads above six throughout the game, only to have the Sharks come back at them every time.
They had to work their way out of their dangerzone with time nearly up, but lost the ball late in the tackle count.
From the scrum win the Sharks spread the ball wide immediately, only for the key tackle to be made, and then the Mustangs defence held for two more tackles to seal the win.
Having originally been named on the bench, Whanganui Boxon's Tautahi Rawiri started in the second row and scored a try while kicking five straight conversions.
"He was a big part of our game, made some tough carries," said Reweti.
Fellow Boxon players in centre Jordan Davis and fullback Emitai Logadraudrau also scored tries, as did Linton-based standoff Shadow Wirori and centre Nikolao Ioane.
While waiting to see if they stay alive in the National Championship, the Mustangs are looking to organise a non-competition game with Coastline, from Tauranga, on September 8, although this has yet to be confirmed.